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Geometric Complexity Theory has demonstrated that Complexity Theorists should care about Algebraic Geometry and Representation Theory, but, why should Algebraic Geometers and Representation Theorists care about Geometric Complexity Theory?

More concretely: what does Geometric Complexity Theory tell us about Algebraic Geometry and Representation Theory that is non-trivial?

note: of course Algebraic Geometers and Representation Theorists qua Mathematicians should care when their fields are applied to important issues in other fields (& they should even care about important issues in other fields that have no known connection to their fields!!!) ... I'm just asking specifically about the transit from Computational Complexity Theory to Algebraic Geometry and Representation Theory because when there is a bridge it is natural to ask about information transit in both directions, and the direction addressed here has been addressed much less than the other direction.

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